Michael Molloy

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Given a sequence of non-negative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n ver-tices of degree i. Essentially, we show that if P i(i?2) i > 0 then such graphs almost surely have a giant component, while if P i(i?2) i < 0 then almost surely all components in such graphs are small. We can apply these results(More)
Given a sequence of non-negative real numbers 0 ; 1 ; : : : which sum to 1, we consider a random graph having approximately i n ver-tices of degree i. In 12] the authors essentially show that if P i(i ? 2) i > 0 then the graph a.s. has a giant component, while if P i(i ? 2) i < 0 then a.s. all components in the graph are small. In this paper we analyze the(More)
In the last few years there has been a great amount of interest in Random Constraint Satisfaction Problems, both from an experimental and a theoretical point of view. Quite intriguingly, experimental results with various models for generating random CSP instances suggest that the probability of such problems having a solution exhibits a “threshold–like”(More)
Many tasks require evaluating a specified Boolean expression over a set of probabilistic tests whose costs and success probabilities are each known. A strategy specifies when to perform which test, towards determining the overall outcome of . We are interested in finding the strategy with the minimum expected cost. As this task is typically NP-hard — for(More)
Wegner conjectured that the chromatic number of the square of any planar graph G with maximum degree 8 is bounded by (G2) 3 2 + 1. We prove the bound (G2) 3 + 78. This is asymptotically an improvement on the previously best-known bound. For large values of we give the bound of (G2) 3 + 25. We generalize this result to L(p, q)-labeling of planar graphs, by(More)
∗Department of Mathematics, Carnegie Mellon University. Supported in part by NSF grants CCR9024935 and CCR9225008. †Department of Computer Science, University of Edinburgh, The King’s Buildings, Edinburgh EH9 3JZ, Uunited Kingdom. Supported in part by grant GR/F 90363 of the UK Science and Engineering Research Council, and Esprit Working Group 7097 “RAND.”(More)